DIFFERENTIAL CALCULUS - LIMITS AND CONTINUITY

Ø Calculus is about rates of change. Rates of change occur in all the sciences.

Ø Calculus is the mathematics of ratio of change of quantities.

Ø It is also the mathematics of tangent lines, slopes, areas, volumes, arc lengths, centroids, curvatures and a variety of other concepts that have enabled scientists, engineers and economists to model real-life situations.

Limits:

Ø A limit is the value that a function "approaches" as the input "approaches" some value.

Ø Limits are essential to calculus and are used to define continuity, derivatives, and integrals.

One sided limits:

Infinite limits and limits at infinity:

Continuity:

Ø One of the chief features in the behaviour of functions is the property known as continuity.

Ø It reflects mathematically the general trait of many phenomena observed by us in nature.

PROBLEMS

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SUMMARY